The incoming chairman of the Senate Judiciary Committee is confident President Donald Trump’s nominee to be attorney general is committed to letting the special counsel probe led by Robert S. Mueller III run its course.

William P. Barr, who previously served as attorney general during the presidency of George H.W. Bush, made the rounds Wednesday on Capitol Hill, where his meetings included visits to the outgoing and incoming chairmen of the Judiciary Committee.

After stopping by the office of Sen. Charles E. Grassley of Iowa, who is trading the Judiciary gavel for Finance, Barr moved on to visit with Sen. Lindsey Graham of South Carolina.

Graham, whom Republicans have selected for the Judiciary chairmanship, told reporters he was very quick to ask Barr about the special counsel’s work.

“I can assure you he has a very high opinion of Mr. Mueller, and he is committed to letting Mr. Mueller finish his job,” Graham told reporters after the meeting.

Such assurances have taken on increased meaning with the reports that Deputy Attorney General Rod Rosenstein is looking to leave the Justice Department once Barr is confirmed. (Rosenstein appointed Mueller to look into Russian efforts to interfere in the 2016 U.S. elections.)

And Graham effectively confirmed the reporting about the pending Rosenstein departure.

“He has a high opinion of Rod. They talked. Mr. Rosenstein mentioned to him, when they first met, I think, that two years would probably be enough,” Graham said. “I trust his judgement to find a worthy successor to Mr. Rosenstein.”

Graham apparently spent much of the meeting with Barr talking about the headline issue.

“I think the main thing that people want to know is what’s his view of the Mueller investigation, and I can assure you, based on what I heard, that he has a high opinion of Mr. Mueller, believes that Mr. Mueller is doing a professional job, will do a professional job and be fair to the president, the country as a whole,” Graham said. “And has no reason for Mr. Mueller to stop doing his job, and is committed to allowing Mr. Mueller to finish.”

But the assurances may not be enough for Democrats, since Graham also said he shared concerns raised by Barr about the possibility of a “slippery slope” from potentially alleging obstruction of justice against a president for firing a political appointee.

Trump, of course, dismissed FBI Director James B. Comey.

But Graham said Barr’s concerns as a private citizen about the possibility of such charges would not be cause for recusal from oversight of the Mueller probe.

“As attorney general, his job will be to receive Mr. Mueller’s report and determine what to do with it,” Graham said.

Graham was among the bipartisan group of senators who announced Tuesday that they were reintroducing a bill designed to protect Mueller or a future special counsel from improper dismissal by Trump or a future president. That measure still has few prospects for getting a Senate floor vote.